If the length of a rectangle is x-2 and its area is 2x3 – 8x2 + 2x+12, it’s width would be what?

Width would have to be a quadratic
Use long division to find the other factor of the cubic polynomial P (x).
P (x) factors in case it is reducible over R[x]
if it weren't then P (x) mod R [x] would be a field
otherwise you could use the Eisenstein Criterion.